clearl 6(7^k) is a multiple of 6 , thus divisible by 6
and in 3(4^k) , the 4^k must be even and any even times 3 is divisible by 6
so we have shown that the result is divisible by 6
(the sum of multiples of 6 must be divisible by 6)
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1) - 2^5(1) = -7, which is divisible by 7. For the inductive case, assume k ≥
Use mathematical induction to prove that 5^(n) - 1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, -1 = -5 +4 This is a take home test so I don't want the
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³ - 5(1) = 6, which is
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